THEORIES OF ECONOMIC GROWTH AND SOME...

THEORIES OF ECONOMIC GROWTH AND SOME

APPLICATIONSDr. Iñaki Erauskin

[email protected] February 2019

Course materials atpaginaspersonales.deusto.es/ineraus/PhD.htm 1

For inspiration

• “Is there some action a government of India could take that would lead the Indian economy to grow like Indonesia’s or Egypt’s? If so, what, exactly? If not, what is it about the “nature of India” that makes it so? The consequences for human welfare involved in questions like this are staggering: once one starts to think about them, it is hard to think about anything else”.Robert E. Lucas Jr. (1988) “The mechanics of economic

development”, Journal of Monetary Economics, 22:3-42 (p. 5). Nobel Prize winner in Economics 1995. 2

For inspiration

• “Productivity isn’t everything, but in the long run it is almost everything. A country’s ability to improve its standard of living over time depends almost entirely on its ability to raise its output per worker.”

Paul Krugman (1994; p. 9), The Age of Diminishing Expectations. Nobel Prize winner in Economics 2008.

3

INDEX

1. Introduction2. Some facts3. Three waves (Five models):

– 1st wave: The Harrod-Domar model (1)– 2nd wave: The neoclassical model (2)– 3rd wave: Endogenous models

• Investment based: The AK endogenous model (3)• Innovation based:

– The product variety model (4)– The Schumpeterian model (5) 4

INDEX

4. Empirical evidence5. Three (personal) practical examples:

– Growth accounting– Financial globalization/Openness

• Current account behavior.• Inequality.• …

6. Conclusions5

1. INTRODUCTION

6

INTRODUCTION

• Economic growth is a fundamental branch of (macro)economics.

• It focuses on the long-run trend performance of GDP growth (as opposed to business cycles).

• The literature is vast, intuitively quite simple, but mathematically very demanding.

7

2. SOME FACTS

8

For discussion

• Please look at the data provided by Angus Maddison.

• Which are the main trends shown by thedata?

• Please note “The rule of 70”: a country growing at a g rate, will double GDP per capita in 70/g years.

11

GDP per capita, 1850-2016

Source: Angus Maddison Project Database 2018 (https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2018 ).

12

0

10000

20000

30000

40000

50000

60000

1850

1854

1858

1862

1866

1870

1874

1878

1882

1886

1890

1894

1898

1902

1906

1910

1914

1918

1922

1926

1930

1934

1938

1942

1946

1950

1954

1958

1962

1966

1970

1974

1978

1982

1986

1990

1994

1998

2002

2006

2010

2014

GD

P pe

r ca

pita

(201

1US$

)GDP per capita (2011US$), 1850-2016

Spain

USA

UK

GDP per capita, 1850-2016

Source: Angus Maddison Project Database 2018 (https://www.rug.nl/ggdc/historicaldevelopment/maddison/releases/maddison-project-database-2018 ).

13

y = 0.0176x + 7.216R² = 0.8773

y = 0.0184x + 7.8269R² = 0.9859 y = 0.0128x + 8.2236

R² = 0.9482

6

7

8

9

10

11

1218

5018

5418

5818

6218

6618

7018

7418

7818

8218

8618

9018

9418

9819

0219

0619

1019

1419

1819

2219

2619

3019

3419

3819

4219

4619

5019

5419

5819

6219

6619

7019

7419

7819

8219

8619

9019

9419

9820

0220

0620

1020

14

GD

P pe

r ca

pita

(201

1US$

, in

logs

)GDP per capita (2011US$, in logs), 1850-2016

Spain

USA

UK

Lineal (Spain)

Lineal (USA)

Lineal (UK)

Source: Clark, Gregory (2008). A farewell to alms. A brief economic history of the world. Princeton University Press.

14

Important sources of data

• OECD: http://www.oecd.org/• IMF: http://www.imf.org/• World Bank: http://www.worldbank.org/• Eurostat: ec.europa.eu/eurostat• National Statistical Offices.

– For instance, Instituto Nacional de España (INE) for Spain: http://www.ine.es/

15


• Central Banks.– For instance, European Central Bank:

www.ecb.int• EUKLEMS growth and productivity

accounts: http://www.euklems.net/– WorldKLEMS: http://www.worldklems.net/

16


• Penn World Table: https://pwt.sas.upenn.edu/

• The Conference Board: http://www.conference-board.org/

17

Motivation

• OECD November 2012: “Looking to 2060: Long term global growth prospects?” – Main Paper: http://www.oecd-

ilibrary.org/economics/looking-to-2060-long-term-global-growth-prospects_5k8zxpjsggf0-en

– Short paper (policy note): http://www.oecd.org/economy/economicoutlookanalysisandforecasts/2060policynote.pdf

– Video: http://youtu.be/fnIl212tBPk

• What is your opinion, based on the data? 18

Motivation• Robert J. Gordon: “Is US economic growth

over? Faltering innovation confronts the six headwinds” (2012) – Paper: http://www.nber.org/papers/w18315– Shorter reference: http://www.voxeu.org/article/us-economic-

growth-over

• Book: “The rise and fall of American growth: The US standard of living since the Civil War” (2016).

• “Growth pessimist”– What do you think about his views? 19

Motivation

Robert J. Gordon (2012)

20

IR #1 (1750-1830): Steam machines, railroads, …IR #2 (1870-1970): Electricity, internal combustion engines, running water, …IR #3 (1980-): Computers, internet, ICT, …

Motivation• Peter C. Evans & Marco Annunziata “Industrial

internet: Pushing the boundaries of minds and machines” (2012)– Paper: http://files.gereports.com/wp-content/uploads/2012/11/ge-

industrial-internet-vision-paper.pdf– Shorter reference: http://www.voxeu.org/article/next-productivity-

revolution-industrial-internet

• Erik Brynfolsson & Andrew McAfee, “The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies” (2014).

• These are “growth optimists”. 21

Motivation

• Kenneth Rogoff: “Rethinking the growth imperative” (2012)– Opinion: http://www.project-

syndicate.org/commentary/rogoff88/English

• Growth is “compulsory”. • What do you think about his views?

22

Easterlin´s paradox

Source: Easterlin (1974). http://graphics8.nytimes.com/images/2008/04/16/business/Easterlin1974.pdf

Source: Deaton, Angus. “Income, aging, health, and wellbeing around the world. Evidence from the Gallup World Poll. Working paper.

Motivation

• Kenneth Arrow, Partha Dasgupta and others “Sustainability and the measurement of wealth” (2012)– https://www.cambridge.org/core/services/aop-cambridge-

core/content/view/DF1D0473AD397311143DB1033B50A7E6/S1355770X12000137a.pdf/div-class-title-sustainability-and-the-measurement-of-wealth-div.pdf

• An empirical application. • What do you think about their views?

26

Motivation

• Growth versus degrowth: “Living better with less”– My own paper (2012):

http://paginaspersonales.deusto.es/ineraus/Files/ArticuloI%C3%B1akiErauskin_Decrecimiento_Completo.pdf

– Kallis, Kerschner, and Martinez-Alier: “The economics of degrowth” (2012): http://www.sciencedirect.com/science/article/pii/S0921800912003333

27

SOME FACTS

• Some facts (there are many):– Differences in the level of income, and

differences in the rate of income growth among countries.

– Growth is a recent phenomenon.– “Club convergence”.– Poverty reduction. – Inequality reduction, for the world as a whole.

• But more inequality in the developed world (Piketty). 28

Source: Aghion, Philippe, and Peter Howitt (2009). The economics of growth. MIT Press.

29


30


34

3. THREE WAVES(FIVE MODELS)

35

THREE WAVESFIVE MODELS

• There are many frameworks to analyze economic growth. The “correct” model depends on the issue one wants to focus on.

• This talk will be focused on the five main models.

• Aghion and Howitt (2009; mainly Introduction and Part I) will be the main reference in Sections 3 and 4 in this presentation. 36

3.1: THE HARROD-DOMAR MODEL

37

THE HARROD-DOMAR MODEL

• This pertains to the “first wave” in modern economic growth (Harrod 1939, Domar 1946).

• It is a Keynesian inspired growth model.– “Domar was writing in the aftermath of the Great

Depression that made many people running the machines lose jobs. Domar and many other economists expected a repeat of the Depression after World War II unless the government did something to avoid it. Domar took high unemployment as a given, so there were always people available to run any additional machines that you built.” (Easterly, 2001)

38


• According to Easterly (2001), even though it is ignored on a theoretical basis nowadays, it is still used on a practical basis:– “The Harrod-Domar growth model supposedly died

long ago. But for over 40 years, economists working on developing countries have applied (and still today apply) the Harrod-Domar model to calculate short-run investment requirements for a target growth rate. They then calculate a “Financing Gap” between the required investment and available resources, and often fill the “Financing Gap” with foreign aid.”

39


• The main prediction of the Harrod-Domar model is that “GDP growth is proportional to the ratio of investment over GDP”.

• Since output Y was assumed to be proportional to the stock of capital K:

1= tt KαY

40


1 tt KY • Then

1211 ttttt IKKYY

1

1

1

1

t

t

t

tt

YI

YYY

• And the main prediction is given by:

41


• “The problem of balancing aggregate demand and supply was Domar’s concern. Investment in building new machines had a dual character -- it added to desired purchases of goods (demand) and it also added capacity (supply). These two effects would not necessarily be equal, Domar argued, and so the economy would spiral off into either chronic overproduction or chronic underproduction. This was the Harrod-Domarmodel.”– “Knife-edge” condition.

42


• As we will show below, the Harrod-Domarmodel can also be seen as a special case of the AK model.

• The empirical evidence is at odds with the main predictions of the model.

43

3.2: THE NEOCLASSICAL MODEL

44

THE NEOCLASSICAL MODEL

• This is the “second wave” in modern economic growth.

• Today it is the most important benchmark model.

• It has become known as the Solow-Swan model (1956).– Solow is Nobel Prize winner in Economics

1987.45


• In the simplest model, increasing savings increases growth (temporarily), but it cannot last indefinitely.

• In the long run, growth rate is determined by the growth rate of technological progress, which is taken to be EXOGENOUS (independent of economic forces). This exogeneity is an important limitation of the model.

• Underlying principle: diminishing returns or declining marginal product. As more labor/capital is being added, the marginal return eventually falls.

47

Please note the dynamics in a standard growth model

CAPITAL STOCK PRODUCTION

INCOME

SAVINGSINVESTMENT

VARIATION OF CAPITAL STOCK

THE NEOCLASSICAL MODEL• Objective: explaining the evolution of output per

worker L (Y/L or Y/(EL)).• Four elements of the model:1. Standard (Cobb-Douglas) production function,

with constant returns to scale.

Diminishing marginal product is a key element of the model. Additionally, Inada condition, perfect competition, substitutability of factors, and full employment. 49

-1(LE)(K)Y function markets and sbusinesses seconomy' the which with efficiency the and es,technologi modern handle to force

labor the of ability the force,labor the of education and skills Thelabor of EfficiencyLabor

capital ofStock Output

shareLabor 1share Capital

ELKY

THE NEOCLASSICAL MODEL• Four elements of the model:2. Savings S is a fraction of output: S=sY3. Savings=Investment: S=I4. Solow-Swan equation: increase in capital K

depends on investment I minus depreciation K.

50

tttt

ttt

KδsYKK

onDepreciatiIKK

-=-

-=-

1+

1+

3.1: First model: NO technological progress

( ) tttt knδsykk +-=-1+

• Then, in intensive terms (dividing by thenumber of workers, L), we get, after somealgebra, that

tttt+ Kδ-=sY-KK 1

where n is population growth.n denotes the growth rate of population N

Capital letters denote the level of a variable, while lowercase letters denote a variable in intensive terms, i.e., divided by the number of workers: 51

t

tt L

Kk =


• Interpretation:- Capital stock per worker increases with the difference

between gross savings of the economy and the term (+n)k.

- When savings increases investment increases, and capital stock rises.

- (+n)k: the higher the depreciation rate , and populacion growth n, the lower the increase of capital stock per worker.

( ) tttt knδsykk +-=-1+

is known as the Solow-Swan equation

52

Figure- Depreciation plus …

Stock of capital per worker, K/L

Depreciationplus …

per worker

(+n)(K/L)

(+n)(K/L)Depreciation plus …

53

Figure- Production and savings

Stock of capital per worker, K/L

Outputper

workerY/L

Savings perworkers(Y/L)

Productionper worker:Y/L

(Assumption: is constant)

Savings per worker:s(Y/L)

54

Figure – The whole picture

Stock of capital per worker, K/EL

Variableper

worker

s(Y/L)

(+n)(K/L)


The stock of capital per worker increases sincesy>(+n)k

The stock of capital perworker diminishes

since sy<(+n+g)k

Steady state: s(Y/L)-(+n)(K/L)=0

55


• In a balanced equilibrium (steady state):

( ) tttt knδsykk +=⇒=1+

nδs

YK

+=

• This implies that, after some algebra, thestock of capital per worker and capital-output ratio reach a steady state:

56


• For a Cobb-Douglas production function (in intensive terms):

( ) αα ELKLY -1/=

• The level of output per worker is given by

nδs

YK

+=E

YK

LY

1

57


• This implies that:– An increase in savings can increase the rate of

growth transitorily, but not permanently. However, the level of output increases permanently.

– An increase in population growth can reduce the rate of growth transitorily, but not permanently. However, the level of output decreases permanently.

– THERE IS NOT SUSTAINED GROWTH IN THE LONG RUN. 58

3.2. The complete model

tttt kgnyskk ˆˆˆˆ1

• Then, in intensive terms (dividing by theunits of effective workers, EL), we get, after some algebra, that

tttt KsYKK 1

where n is population growth and g is therate of technological progress.n denotes the growth rate of population N and g the growth rate of the level of technology (or efficiency of labor) E. A “hat” denotes the level of a variable in intensive terms, divided by the units of effective workers.

59

tt

tt LE

Kk ˆ


• Interpretation:- Capital stock per effective worker increases with the

difference between gross savings of the economy and the term (+n+g)k.

- When savings increases investment increases, and capital stock rises.

- (+n+g)k: the higher the depreciation rate , and so on, the lower the increase of capital stock per effective worker.


is known as the Solow-Swan equation

60

Figure- Depreciation plus …

Stock of capital per effective worker, K/EL

Depreciationplus …

per effectiveworker

(+n+g)(K/EL)

(+n+g)(K/EL)Depreciation plus …

61

Figure- Production and savings


Outputper effective

workerY/EL

Savings pereffectiveworker

s(Y/EL)

Productionper effectiveworker:Y/EL


Savings per effective worker:s(Y/EL)

62

Figure – The whole picture


Variableper effective

worker

s(Y/EL)

(+n+g)(K/EL)


The stock of capital per effectiveworker increases sincesy>(+n+g)k

The stock of capital per effective worker diminishessince sy<(+n+g)k

Steady state: s(Y/EL)-(+n+g)(K/EL)=0

63


• In a balanced equilibrium (steady state):


gns

YK

• This implies that, after some algebra, thestock of capital per effective worker and capital-output ratio reach a steady state:

64


• For a Cobb-Douglas production function (in intensive terms):

1E

LK

LY

• The level of output per worker is given by

gns

YK

E

YK

LY

1

65


• This implies that:– Long run growth is only determined by the

growth rate of technological change. However, the growth rate of the level of technology is exogenously given.

– In the simplest case where there is no growth in technological progress, for instance, an increase in savings can increase the rate of growth transitorily, but not permanently. However, the level of output increases permanently. 66

THE NEOCLASSICAL MODEL• Based on these results, the model suggests

a testable prediction: Are poor countries likely to catch up with rich ones?

• This has become known as conditional convergence.

• If countries have the same characteristics (technology, ...), the answer is YES for the neoclassical growth model, since they will converge on the same steady state.

67

THE NEOCLASSICAL MODEL• There is a vast literature on this issue,

when compared to the AK model (more on this below).

68


• Additionally, the neoclassical growth model offers a growth accounting framework to quantify the contribution of inputs to output growth (Solow, 1957). More on this will be shown below in Sections 4 and 5.

69


• Please note that this model can be easily extended to incorporate an endogenous savings rate a la Cass-Koopmans-Ramsey. This is the benchmark model in advanced and PhD macroeconomics courses today.

70

3.3: THE AK MODEL

71

NEOCLASSICAL GROWTH MODEL

• In the neoclassical growth model the rate of technological change is assumed to be exogenously given (determined by non-economic forces).

• However, that was clearly unsatisfactory.• Now this is endogenously derived.

72

ENDOGENOUS GROWTH

• However, assuming exogenous technological change was not satisfactory because technological change is surely NOT exogenous. – Instead, it depends on economic decisions (it is

endogenous) since it comes from industrial innovations made by profit-seeking firms.

• It will depend on: the funding of science, the accumulation of human capital, and others economic activities. 73

ENDOGENOUS GROWTH

• In the neoclassical growth model, the fundamental reason to converge to a steady state with zero per capita growth is the diminishing returns to capital.

• Therefore, to attain a positive per capita growth, there should not be diminishing returns to capital. This is a key feature in endogenous growth models.

74

THE AK MODEL

• The AK growth model pertains to the “third wave” in modern economic growth, and, in turn, to the “first family” (investment based) of models since there are others in modern economic growth.

75

ENDOGENOUS GROWTH

• Incorporating endogenous technology into growth theory forces us to deal with the difficult phenomenon of increasing returns to scale: people must be given an incentive to improve technology.– With constant returns to scale, inputs are paid

according to their marginal products. Then there is nothing to pay for the resources used in improving technology.

– Endogenous theory cannot be based on the usual theory of competitive equilibrium. 76

ENDOGENOUS GROWTH• Arrow (1962) proposed a solution:

technological progress is supposed to be an unintended consequence of producing new capital goods, named as “learning by doing” (e.g. airframe manufacturing, shipbuilding, ...). Knowledge creation is a side product of investment. A firm that increases its physical capital learns simultaneously how to produce more efficiently. This positive effect of experience on productivity is called learning by doing (or investing).– Arrow is Nobel Prize winner in Economics 1972.

77

ENDOGENOUS GROWTH• Learning by doing was assumed to be

purely external to the firms responsible for it. – That is, if technological progress depends on

the aggregate production function of capital and firms are all very small, they all can be assumed to take the rate of technological progress as being given independently of their own production of capital goods.

• Each firm maximizes profits paying inputs their marginal products.

• There is not an additional payment for their contribution to technological progress.

78

ENDOGENOUS GROWTH

79

ENDOGENOUS GROWTH• Productivity growth is based on two assumptions:

– Learning by doing works through each firm’s net investment. An increase in a firm’s capital stock leads to a parallel increase in its stock of knowledge, A:

• (Arrow) Knowledge and productivity gains come from investment and productivity, based on empirical evidence that large positive effects of experience on productivity in airframe manufacturing, shipbuilding, and other areas.

– Each firm’s knowledge is a public good that any other firm can access at zero cost. In other words, once discovered, a piece of knowledge spills over instantly across the whole economy.

• The spillover assumption is natural because knowledge has a nonrival character: if one firm uses an idea, it does not prevent others from using it. Of course, firms have incentives to maintain secrecy over their discoveries and patents (then knowledge leaks out gradually). This has been modeled also.

80

THE AK MODEL

• The AK model assumes that when people accumulate capital, learning by doing generates technological progress that tends to raise the marginal product of capital, thus offsetting the law of diminishing marginal product (when technology is unchanged). Then the marginal product is constant, A:

AKY 81

THE AK MODEL

AKY

• The AK model is based on capital accumulation. Thus long run growth ratedepends on economic factors such as thriftand the efficiency of resource allocation.

• Instead, other models of endogenous growth(more on this later) emphasize creativityand innovation as the main drivers of economic growth. 82

THE AK AND THE HARROD-DOMAR MODELS

BLAKLKFY ,min),(

• An early precursor of the AK model was that of Harrod-Domar. If the production function has fixed technological coefficients (Leontiev):

• Due to the non-substitutability of inputs, thethere will probably be surplus capital orlabor.

83


• When capital is the limiting factor (surplus labor takes place) in Harrod-Domar’smodel, i.e., AK<BL, then the productionfunction is “linear-in-K”:

AKY

84


• Then the Solow-Swan equation becomes

• The growth rate of capital will be:tttt KsAKKK 1

sAK

KKgt

tt 1

85

• Since output is linear-in-K, then the rate of growth of output will also be g.

• The growth rate is increasing in the savingsrate s.


• The problem with the Harrod-Domar modelis that it cannot explain the sustainedgrowth in output per person exhibited sincethe industrial revolution.• Growth rate of output per worker = g-n• But if this is positive, the growth rate of capital

per worker K/L, g-n, is also positive. • A point will be reached where capital is not the

limiting factor. Then Y=BL, both Y and Lgrowing at the same rate: output per workerceases to grow.

86

NEOCLASSICAL VERSIONOF HARROD-DOMAR

• The first AK model accounting for sustained growth in output per capita is Frankel (1962). His model encompasses:– Solow: perfect competition, substitutability of

factors, and full employment.– Harrod-Domar: long run growth rate depends

on the savings rate.

87


• The model is based on “Learning by doing”: individual firms contribute to the accumulation of technological knowledge (development) when they accumulate capital (spillover effects: aggregate productivity depends on firms’ specific-sectoral productivity).

1jjj LkAy

N

jjkAA

10

reflects the extent of the knowledge externalities generatedamong firms (if =0 there are not externalities)

88


• Once output, capital, and labor are aggregated across firms, the result is that, in equilibrium, aggregate output is given by:

AKY

tttt KsAKKK 1

• Thus

11

tt

tt sAKK

KK89


• And the growth rate of capital is given by

11t

t

tt sAKK

KKg

90


• Depending on the impact of diminishing returns and the spillover effect: – Diminishing returns are stronger (+<1): Solow-

Swan results. Stable steady state. Long run growth rate is zero.

– Spillover results are stronger (+>1): ever increasing growth rate. Unstable steady state. Explosive growth.

– Both impacts compensate (+=1): AK model results, Y and K increase in the same proportion, but with substitutability of factors, full employment. Thus:

91

sAK

KKgt

tt 1


• Please note that intertemporal utility maximization can be easily incorporated to the model.

92

THE AK MODEL

• There is a vast literature on the empirical debate between between neoclassical and AK growth models:– Persistent positive growth rates of per capita GDP in

most countries worldwide. This fact can be explained by the AK growth model, but not by the neoclassical model.

– Cross-country or cross- regional convergence, either absolute (irrespective of their characteristics) or conditional (given similar characteristics). This runs in favor of the neoclassical model. Club convergence.

93


94

THE AK MODEL

• An underlying difficulty for the AK modelis that there is no explicit distinctionbetween capital accumulation and technological progress.

• The next models focus mainly oninnovation-based models that make thatdistinction explicit.

95

3.4: THE PRODUCT VARIETY MODEL

96

THE PRODUCT VARIETY MODEL

• This is the third wave in modern economic growth: innovation-based (“second family”) growth models related to product variety (Romer, 1990).

• Innovation causes productivity growth by creating new, but not necessarily improved, varieties of products.

97


• Productivity comes from an expanding variety of specialized intermediate products. Product variety expands gradually because discovering how to produce a large range of products takes real resources, including time.

• Growth is induced and sustained by increased specialization (A.A. Young, 1928). 98


• For each new product there is a sunk cost of product innovation that must be incurred just once, when the product is first introduced, and never again. The sunk costs can be taken as costs of research, an activity that adds to the stock of technological knowledge.

99


• Technological knowledge consists of a list of blueprints, each of them describing how to produce a different product, and every innovation adds one more blueprint to the list (understood as basic innovation, as if a new industry were opened up). Identifying the state of the technology with the number of varieties should be seen as a metaphor.

100


• Differences with AK model:– Sunk cost of product development, AND– Fixed costs make product markets

monopolistically competitive rather than perfectly competitive. Imperfect competition creates profits, and these profits act as a reward for the creation of new products.

• This allows to “solve” the problem created by Euler’s theorem (given that perfect competition exhausts income). 101


• Elements of the basic model:– Consumers. Utility maximizers.– Firms. Profit maximizers.

• Research sector. Perfect competition. Spending on researchcreates new blueprints (that is, expands the number of varieties). A blueprint has a value for its inventor.

• Producers of intermediate goods, which are different fromeach other. Each interm. good is monopolized by the personwho created the blueprint.

• Producers of final goods. Perfect competition. Intermediategoods are used as inputs. The final good is devoted toconsumption, production of blueprints, and production of interm. goods.

102


• Final output is produced under perfect competition using labor and a range of intermediate inputs . The final goods production function is:

tN

iittt xLY

0

1

• There are N varieties of intermediateproducts, and xit refers to units of intermediate input (capital). 103


• The production function exhibits diminishing marginal products of each input but constant returns to scale in all inputs together.

• The function is additively separable: marginal products of intermediate goods are independent. New discoveries do not convert others obsolete.

tN

iittt xLY

0

1

104


tN

iittt xLY

0

1

• Each intermediate product is producedusing the final good as input, one for one. That is, each unit of intermediate product iproduced requires the input of one unit of final good.

105


tttt xNLY 1

106

Thus product variety N enhances overall productivity in the economy. Technological change in the form of continuous increases in N avoids the tendency for diminishing marginal returns. This is the basis for endogenous growth.

Adding up:


tN

iit xX

0

Xt is the total amount of final good used in producingintermediate products.

• Suppose that each intermediate product isproduced in the same amount x (in equilibrium). Then

t

t

NXx

107

By symmetry, aggregate stock of capital Xt is divided into the Ntvarieties evenly.


• Substituting

tttt XLNY 11

108

t

t

NXx

into

tN

iittt xLY

0

1

we get


• Given L, if intermediates Nx expand:– Taking the form of increases in x, diminishing

returns are found.– However, with increases in N diminishing

returns do not arise.• Increasing N encompasses technological

change: diminishing returns do not take place. Endogenous growth occurs. 109

tttttttt xNLNXLNY 1111


• The degree of product variety is the economy’s aggregate productivity parameter, and its growth is the long-run growth rate of per capita worker.

• More product variety raises output potential because a given capital stock is spread over a large number of uses, each of which shows diminishing returns. 110

tttttttt xNLNXLNY 1111


• Increasing product variety sustains growth.• New varieties (new innovations) themselves

result from R&D investments by research-entrepreneurs, who are motivated by the prospect of (perpetual) monopoly rents if they successfully innovate.

• There is only one kind of innovation, which always results in the same kind of new product.

111


• The empirical evidence does not seem to provide a strong support for this model.

• In addition, there is no role for exit and turnover in the economy.

112

3.5: THE SCHUMPETERIAN MODEL

113

THE SCHUMPETERIAN MODEL

• This is the third wave (“third family”) in modern economic growth. Again this is an innovation-based growth model, also known as the Schumpeterian model since it involves “creative destruction” (Schumpeter, 1942): quality-improving innovations created by new technologies render old products obsolete (Aghion and Howitt, 1992, 1998).

115


116


• The model begins with a Cobb-Douglas type of production function at the industry level

ititit KAY 1

117

• K represents the flow of a unique intermediate product used in this sector, each unit of which is produced one-for one by final output (or capital).


• Each intermediate product is produced and sold exclusively by the most recent innovator (a monopolist). A successful innovator in sector i improves the technology parameter Ait and is thus able to displace the previous product in that sector, until it is displaced in turn by the next innovator.

118


• First implication of the model: faster growth generally implies a higher rate of firm turnover, because this process of creative destruction generates entry of new innovators and exit of former innovators.

119


• Even though the focus is on individual industries, the assumption that all industries are equal ex ante offers a simple (Cobb-Douglas) structure.

ttt KAY 1

120

• As in the neoclassical model, the long run growth rate is given by the growth rate of the factor productivity A, which here depends endogenously on the economy-wide rate of innovation.


• There are two main inputs to innovation:– The private expenditures made by the

prospective innovator, and– The stock of innovations that have already been

made by past innovators: publicly available stock of knowledge (current innovators can add to it).

ttt KAY 1

121


– (Cont.) Stock of innovations available:• An innovation that leapfrogs (“salto de rana”) the best

available technology available before the innovation, resulting in a new technology parameter Ait in the innovating sector i, which is some multiple of its preexisting value: LEADING-EDGE INNOVATION.

• An innovation that catches up to a global technology frontier Ât(the stock of global technological knowledge available to innovators in all sectors in all countries). IMPLEMENTING (IMITATING) INNOVATION

ttt KAY 1

122


• If leading-edge innovations take place at the frequency n and implementation innovations (or imitations) at the frequency m, then the aggregate productivity parameter evolves as

ttmtntt AAAAA 11

123

Frequency = Probability of an innovation in each period (also the long-run frequency of innovations , that is, the fraction of periods in which an innovation will occur).γ-1= The proportional increase in productivity resulting from each innovation.

frontiery technologglobal a torefers tA


• And the growth rate will be given by

11 11

tmn

t

ttt a

AAAg

ttmtntt AAAAA 11

where

t

tt A

Aa

is an inverse measure of “distance to thefrontier” 124


• Growth policies are highly context-dependent:– How does country performance vary with its

proximity to the technological frontier at?– To what extent will the country converge to the

technological frontier at?– What kinds of policy changes are needed to

sustain convergence as the country approaches the technological frontier at?

11 11

tmn

t

ttt a

AAAg

t

tt A

Aa

125


• The critical innovation frequencies could be:– Taken as given, or,– Derived endogenously from profit maximization

strategies. They will depend on:• Economic institutions, such as property right protection, the

financial system, ...• Government policy.

• The equilibrium intensity and mix of innovation will depend on the institutions and policies, and this in turn from the country´s distance to the technological frontier.

126


• This is Gerschenkron´s “advantage from backwardness” (1962): the further the distance, the faster the growth rate, given the frequencies.

• Appropriate institutions can also be easily incorporated in the framework. If institutions favoring imitation are not the same as those favoring leading-edge innovation:– If far from the frontier: imitation. – If close to the frontier: leading-edge innovation.

11 11

tmn

t

ttt a

AAAg

127

SAPIR REPORT

Source: An agenda for a growing Europe. Making the EU Economic System Deliver. Chaired by André Sapir (2003). European Commission.

128

SAPIR REPORT

Source: An agenda for a growing Europe. Making the EU Economic System Deliver. Chaired by André Sapir (2003). European Commission.

129

TO RECAP: MODELS• First wave: Harrod-Domar (capital accum.).• Second wave: Solow-Swan (capital

accum.).• Third wave:

– First family: AK model (based on capital accumulation).

– Second family: Product variety (innovationbased).

– Third family: Schumpeterian model (innovationbased).

130

4. EMPIRICAL EVIDENCE

131

EMPIRICAL EVIDENCE

• Neoclassical and AK growth models focus on capital accumulation, while product-variety and Schumpeterian models focus on innovations that raise productivity.

• Two have been the main strands of empirical analysis:– Convergence (econometric). Mentioned for neoclassical

vs. AK.– Growth accounting (non-econometric and

econometric). This is the topic I will analyze now.

132

EMPIRICAL EVIDENCE

• Growth accounting. Solow (1957). – Which is the contribution of inputs to output?

Which are the sources of growth?– General framework based on Solow (1956).

First results focus on total factor productivity (TFP) growth. Capital accumulation is also an important factor.

– Measuring capital is difficult.– Accounting for vs. Causation.

133


134

EMPIRICAL EVIDENCE

• Directions of new research in growth accounting: – Human capital, – Information and Communication Technologies

capital, and– Intangible assets.

• I will focus on the basic framework in the next section in more detail.

135

5. THREE (PERSONAL) PRACTICAL EXAMPLES

136

THREE (PERSONAL) PRACTICAL EXAMPLES

• Broad recommendation for research: provide a coherent mix of theory and empirical evidence. It makes it much easier to “sell”.

137

5.1: GROWTH ACCOUNTING

138

GROWTH ACCOUNTING

• What follows is mostly based on Erauskin(2011): “ACCOUNTING FOR GROWTH IN SPAIN, THE BASQUE COUNTRY (AND ITS THREE HISTORIC TERRITORIES), NAVARRE, AND MADRID SINCE 1965”. – An older paper in 2008 on this issue as well.

139

Introduction

• Motivation:– Post-war period has been a fruitful period as far

as economic progress is concerned.– However, growth did not proceed at a steady

pace.– Territories throughout Spain have performed

unevenly.– Few studies on the whole period 1965-2008.

140

Introduction

• This paper provides a long term analysis on the proximate causes of economic growth for 1965-2008.– Spain, the Basque Country, Navarre, Madrid,

the EU, and the US.

141

The growth accounting methodology

• How does it work? Proximate sources of economic growth (vs. Deep determinants of growth).

• Growth accounting decomposes the growth rate of output into:– Contribution of labor growth.– Contribution of capital growth.– Everything else: “black box”; “measure of our

ignorance”, growth in total factor productivity, …• Origins: Solow (1957).

142


• Neoclassical production function: ,K,K,K,LFAY t,Ot,ICTt,INFttt

Y=OutputA=Level of technology (TFP)L=LaborK=Services of capital

• Infrastructures (INF),• Information and Communication Technologies

(ICT): hardware, software, and communications, • Others (O).

143


K=Services of capital• Infrastructures (INF): road, water, railway, airport,

port, and urban.• Information and Communication Technologies

(ICT): – Hardware: office machinery and computer equipment,– Software, and– Communications

• Other (O) type of non-residential capital:– Constructions other than dwellings and the infraestructures

referred to earlier,– Transport equipment.– Machinery, equipment and other products, except ICT.

144


• Under usual assumptions, the growth rate of output is:

tOtKO

tICTtKICTtINFtKINFttLtt

KKKLAY

,,

,,,,,

lnlnlnlnlnln

where denotes input shares.

• If we have data on Y, L, and K, and input shares...

145


Then ...

tOtKO

tICTtKICTtINFtKINFttLtt

KKKLYA

,,

,,,,,

lnlnlnlnlnln

= the growth rate of output that cannot beattributed to the (weighted) growth rate of inputs=“Solow residual”=“a measure of ourignorance”=technical innovations, organizational and institutional changes, changes in societal attitudes, fluctuations in demand, changes in factor shares, omittedvariables, and errors of measurement.

146


• Alternatively:

ttOtKOttICTtKICT

ttINFtKINFttt

LKLKLKALYlnlnlnln

lnlnlnlnln

,,,,

,,

which is very useful to analyze the growth rate of output per hour (or per worker).

147


• The above equations have been obtained using non-econometric procedures:– They are the most frequently used.– Important advantages over econometric

procedures.

148

Results of previous studies

• Several studies for Spain, but very few for the Autonomous Communities, or provinces in Spain.

• Escriba and Murgui (1998). Growth in TFP and private capital were the sources of growth (1980-1993).

• Gallastegui (2000). Period 1985-1994. 60% was explained by the evolution of private and public capital, employment, training of workers, and expenditure in R+D. 30% was explained by technological change. 149


• Goerlich and Mas (2001). Growth in TFP was the main source of growth, followed by private capital (1965-1996).

• Timmer, Ypma and van Ark (2003). 1980-2001– EU: Growth in TFP and capital during 1980-1995.

Increasing contribution of labor during 1995-2001. ICT contribution increased, but not much.

– US: Growth in labor and capital during 1980-1995, and capital and labor during 1995-2001. ICT contribution increased notably.

– Spain: similar sources to those of the EU. Growth in TFP during 1980-1995, and labor during 1995-2001. ICT contribution did not increase.

150


• Mas and Quesada (2005). Similar results to those of Timmer et al. (1985-2002).– Labor and capital were the main sources of growth.– The contribution of labor increased enormously, while

that of TFP declined. – Increasing contribution of ICT capital.

• Erauskin (2005). 1986-2000. Private capital and TFP growth fuelled output growth in the Basque Country.

151


152


153

Results of previous studies• Van Ark, O’Mahony, & Timmer (2008).

– “the European productivity slowdown is attributable to the slower emergence of the knowledge economy in Europe compared to the United States”.

• Lower contribution of ICT capital.• Lower share of technology-producing industry in the

EU.• Lower TFP.

– Working of labor market. High product market regulation. 154

Results of previous studies• Pérez & Robledo (2010). Spain, 1970-2007

– Contribution of capital and labor.– Difference: Declining role of TFP growth.

Causes:• Too much investment in the building sector.• Additional orientation of investment: services.• Deficiencies in education and inadequate working of

labor market.• Unproductive overinvesment in productive assets.

155

Results of previous studies• Erauskin (2008). Spain, the Basque

Country, and Navarre, 1986-2004.– Higher growth rates for 1995-2004.– Labor and capital growth rates were the main

engines of growth. – TFP growth was residual and it was declining,

even reaching negative figures.

156


157

Data sources• Data for the EU and the US: EU KLEMS.

From 1970 (1980) onwards.• Data for Spain:

– National Accounts.• INE.• FBBVA. For data before 1986.

– FBBVA and IVIE: new capital database from 2007 onwards (period 1964-2008).

• Data for the Basque Country (GVA, employment). Independent data from 1980 onwards. 158

The results• Three periods:

– 1965-1975: “Traditional catch-up pattern”– 1975-1995: “Productivity slowdown”– 1995-2008: “Europe’s falling behind”.

159

Different sources of data for the Basque Country

164

Conclusions

1. Growth rates of output.• They were high in the whole period 1965-

2008.2. They were spectacular during 1965-1975.

Sources of economic growth. • Capital and TFP were the main sources of

growth during 1965-2008.• TFP growth played a residual and declining

role in the most recent period 1995-2008.168

Conclusions

3. Some caution on the results for the Basque Country.

• The annual average growth rate of GVA is between 0.25 and 1 % higher if data from Eustat are used, due to differences in GVA deflators (mainly recently) and values in current prices.

169

Conclusions

4. There was an important improvement in the economic performance during 2003-2007, especially for the Basque Country. A “golden-four-year-growth-period”

5. The recent crisis has broken with the expansion period.

170

5.2: CURRENT ACCOUNT BEHAVIOR

171

CURRENT ACCOUNT BEHAVIOR

• Erauskin (2009): “THE CURRENT ACCOUNT AND THE NEW RULE IN A NOT-SO-SMALL OPEN ECONOMY”

172

INTRODUCTION

• Motivation: huge movements in cross-border holdings of financial assets, and their implication on the behavior of current accounts.

• “The intertemporal approach views the current-account balance as the outcome of forward-looking dynamic saving and investment decisions” (Obstfeld & Rogoff).

ICA S 173

INTRODUCTION

• Which is the impact of a transitory income shock (fluctuations in output, for example) on the current account?– Traditional rule: the impact is equal to the amount of

savings generated by the shock. However, it does not hold empirically.

– New rule: the impact is equal to the amount of savings generated by the shock multiplied by the net foreign asset position. It seems to hold empirically. The original idea was proposed by Kraay and Ventura (2000).

174

INTRODUCTION

• However, it is assumed that the country is a small open economy.

• Contribution of the paper:– Extending the new rule to a not-so-small open

economy: which is the impact of transitory income shocks on the current account in a not-so-small open economy (i.e. in a two-country world)?

– Empirically test the main predictions: how does the theory fit with the empirical data? 175

THEORY

• Endogenous growth: domestic and foreign capital is subject to diminishing returns to capital. Aggregate capital stock has an external effect on labor productivity, but the firm faces decreasing returns to capital. – “We motivate diminishing returns to domestic capital

bluntly as the result of congestion effects or negative externalities. Since the representative consumer is infinitesimal, he/she understands that his/her actions have no influence on the aggregate stock of capital.” (Kraay and Ventura, 2000). 176

THEORY

• Two countries.• Stochastic shocks. This feature permits

incorporating risk to the analysis. Mean-variance approach.

• Continuous time.

177

THEORY

• One homogeneous good.• Three assets:

– Risky domestic capital,– Risky foreign capital, and– Bonds: risk free endogenous interest rate.

178

THEORY

BKKW

BKKW

ff

dd

**

*• Domestic and foreign wealth:

179

• Domestic wealth:• Domestic capital in the hands of the domestic economy.• Foreign capital in the hands of the domestic economy.• Net position of risk-free loans.

• Foreign wealth:• Domestic capital in the hands of the foreign economy.• Foreign capital in the hands of the foreign economy.

THEORY• Net foreign asset position:

BKKP fd *

• The current account is equal the variation in its net foreign asset position:

dBdKdKdPCA fd *

180

THEORY

• The current account balance is equal to the variation in domestic wealth (that is, savings ) minus the variation in domestic capital (domestic net investment).

**

WK

dWWKdWdWdKdWISCA fd

181

THEORY

• When a transitory income shock occurs:– Part of the shock is consumed.– Part of the shock is saved:

• Traditional view: countries invest the marginal unit of wealth in foreign assets, when risk associated with investment is low compared to the diminishing returns effect.

• New view: countries invest the marginal unit of wealth as the average one, when risk associated with investment is high compared to the diminishing returns effect.

**

WK

dWWKdWdWdKdWISCA fd

182

THEORY: The three results

**

WK

dWWKdWdWCA fd

1) Traditional view: 0

WKd

2) New view:WK

WK dd

0fdK• Small open economy:

3) Not-so-small open economy: ** WK

WK ff

183

TRADITIONAL RULE

dWCA

• Traditional view: 0

WKd

• Result: the impact of transitory income shocks on the current account is equal to the saving generated by the shock.

• Small open economy: 0fdK

184

NEW RULE

WBKdW

WKdWdWCA dd

*

• New view: WK

dWdK dd

• Result: the impact of transitory income shocks on the current account is equal to the saving generated by the shock multiplied by the net foreign asset position of the country.

• Small open economy: 0fdK

185

EXTENDED NEW RULE

**

*

**

WK

dWW

BKdWWK

dWWKdWdWCA fdfd

• New view: WK

dWdK dd

** WK

WK ff

• Not-so-small open economy:• Result: the impact of transitory income

shocks on the current account is equal to the saving generated by the shock multiplied by the net foreign asset position of the country plus a new term. 186

DATA SOURCES

• Complex issue• Sample: 19 OECD countries (1970-2004).• The data are based on:

– International Monetary Funds´s International Financial Statistics

– World Bank´s World Development Indicators, and

– Lane and Milesi-Ferretti (2007).187

EMPIRICAL EVIDENCE

188

EMPIRICAL EVIDENCE

189

EMPIRICAL EVIDENCE

190

EMPIRICAL EVIDENCE

191

EMPIRICAL EVIDENCE

192

EMPIRICAL EVIDENCE

193

CONCLUSIONS

• Increasing financial integration has important implications for the current account.

• The traditional rule has failed to account for the empirical evidence on current accounts.

• KV provided an insightful departure from the traditional rule: the new rule. Moreover, the empirical evidence seemed to validate the new rule. However, it is based on a small open economy assumption. 194

CONCLUSIONS

• The paper has suggested an extension to the new rule rule abandoning the small open economy assumption. It is broadly supported by the empirical evidence, which seems to reject the new rule.

195

CURRENT ACCOUNT BEHAVIOR

• Erauskin (2015): “SAVINGS, THE SIZE OF THE NET FOREIGN ASSET POSITION AND THE DYNAMICS OF CURRENT ACCOUNTS”.

MOTIVATION

• Big current account imbalances in recentyears.

• Huge variations in gross and net international investment positions.– Consequences for current accounts are

straightforward.

INTRODUCTION

“The intertemporal approach views thecurrent-account balance as the outcome of forward-looking dynamic saving and investment decisions”.

ICA S

INTRODUCTION

• Which is the impact of a transitory income shock (fluctuations in output, for example) on the current account? There are two main views: – Traditional rule (standard benchmark model):

• This view is appropriate when domestic capital is subject to diminishing returns and risk associated to investment is low.

• The marginal unit of wealth (savings) is invested in foreign bonds.

– Then the impact on the current account is equal to the amount of savings generated by the shock.

• However, the traditional rule does not hold empirically. Feldstein-Horioka puzzle. 199

ctctct uSaaCA 10

INTRODUCTION

• Two main views (cont.):– New rule:

• The original idea was proposed by Kraay and Ventura (2000).• This view is appropriate when risk associated to investment is

high compared to the diminishing returns effect. • The marginal unit of wealth (savings) is invested as the

average unit of wealth.• Please note:

– Then the impact is equal to the amount of savings generated by the shock multiplied by the net foreign asset position. 201

WP

WP

WK

WK

WP

WK

onset positiforeign asNetPPKW

ddd

d

;;1

;

ctctct

ctct uS

WPaaCA

10

INTRODUCTION• This paper offers three main contributions:

– We adapt the new rule to distinguish between gross and net foreign asset positions, because both matter.

– We combine both the new view and the traditional rule.– The empirical evidence suggests that the support for the

traditional rule or the new view depends crucially on the size of the net foreign asset position.

• Intermediate case: the new view dominates.• “Big” creditor (+15% domestic wealth) case: the traditional

rule dominates.• “Big” debtor case (-15% wealth) case: the traditional rule

dominates, but the impact is much weaker than for creditors. 203

STRUCTURE OF THE PAPER

1. Introduction.2. Theory.3. Data sources.4. Empirical evidence.5. Conclusions.

THEORY• Endogenous growth.

– Capital is subject to diminishing returns. Aggregate capital stock has an external effect on labor productivity, but the firm faces decreasing returns to capital.

• Two countries.• Two assets:

– Riskless domestic capital, and– Risky foreign capital.

• Stochastic shocks in the foreign economy. Mean-variance approach.

• Continuous time. 205

THEORY

**

*

ff

dd

KKWKKW

• Domestic and foreign wealth:

206

• Domestic wealth:• Domestic capital in the hands of the domestic economy.• Foreign capital in the hands of the domestic economy.

• Foreign wealth:• Domestic capital in the hands of the foreign economy.• Foreign capital in the hands of the foreign economy.

THEORY

,;0,;1 0 11

11

0

CdteCEMax t

• Preferences (Stone-Geary):

207

subject to:

dtCdyKdtKKdW ddd*****

THEORY

1/12

*

*

WWK

y

d

• Solution for the domestic economy:

208

2

2*

2

2*

*

*

15.0

115.0

y

y

WC

• Analogous for the foreign economy.

THEORY• Net foreign asset position:

fd KKP *

• The current account is equal the variation in its net foreign asset position (savings minusinvestment):

**

* 1 dWWKdW

WKdKdKdPCA fd

fd

209

THEORY

w

K

WKWK d

y

d

d

2*

/1

1

210

• How do countries react?

2*

/

y

dK

is key.

– If big, – If small,

0WKd

w

KWK dd

THEORY

**

WKdW

WKdWdWCA fd

WK

WK dd

Then:

211

** WK

WK ff

**

*

1 dWWKdW

WKdWCA fd

• How do countries react?

10

DATA SOURCES

• Complex issue. Domestic wealth.• Sample: 50 developed and developing

countries (1970-2009).• The data are based on:

– International Monetary Funds´s International Financial Statistics

– World Bank´s World Development Indicators, and

– Lane and Milesi-Ferretti (2007). 212

EMPIRICAL EVIDENCE

213

ctctct uSaaCA 10

EMPIRICAL EVIDENCE

214

ctctct

ctct uS

WPaaCA

10

EMPIRICAL EVIDENCE

215

EMPIRICAL EVIDENCE

216

ctctct

ctct uS

WPaaCA

10

EMPIRICAL EVIDENCE

EMPIRICAL EVIDENCE

218

ctctct

ctct uS

WPaaCA

10

EMPIRICAL EVIDENCE

219

ctctct

ctfct

ct

ctdctct uS

WK

aSWK

aSaaCA

*

*,

3

*,

210

EMPIRICAL EVIDENCE

220

ctctct

ctfct

ct

ctdctct uS

WK

aSWK

aSaaCA

*

*,

3

*,

210

EMPIRICAL EVIDENCE

221

ctctct

ctfct

ct

ctdctct uS

WK

aSWK

aSaaCA

*

*,

3

*,

210

CONCLUSIONS

• The combination of the traditional rule and the new view provides a satisfactory framework to explain the dynamics of current accounts, when the size of the NFA is considered:

• Moderate size: the new view dominates.• “Big” creditor: the traditional rule dominates. • “Big” debtor: the traditional rule dominates, but the

impact is weaker.

• Future research: Bigger sample, recent crisis, … 222

6. CONCLUSIONS

223

CONCLUSIONS

• The literature on economic growth has provided many fruitful insights on many issues.

• However, many others remain unanswered, suggesting avenues for future research.

• When addressing an issue for research, I would recommend an appropriate mix of theoretical (adopting a model suitable for the objectives planned) and empirical contents.

224

REFERENCES

225

REFERENCES (Textbooks)

• Aghion, Philippe and Peter Howitt (1998), Endogenous growth theory, MIT Press.

• Aghion, Philippe and Peter Howitt (2009), Economics of growth, MIT Press.

• Barro, Robert and Xavier Sala i Martín (2004), Economic growth. Second edition,McGraw-Hill. Also in Spanish.

226

REFERENCES (Textbooks)

• Easterly, W. (2001), The Elusive Quest for Growth : Economists ’ Adventures and Misadventures in the Tropics, MIT Press. Also in Spanish.

• Weil, David N. (2009), Economic growth.Second edition, Pearson Addison Wesley.

227

REFERENCES (Others)

• Aghion, Philippe and Peter Howitt (1992), “A model of growth through creative destruction”, Econometrica, 60: 323-351.

• Arrow, Kenneth J. (1962), “The economic implications of learning by doing”, Review of Economics Studies, 29:155-173.

• Domar, Evsey (1946), “Capital expansion, rate of growth, and unemployment”, Econometrica, 14: 137-147.

228

REFERENCES (Others)

• Frankel, M. (1962), “The production function in allocation of growth: a synthesis”, American Economic Review, 52:995-1022.

• Harrod, Roy F. (1939), “An essay in dynamic theory”, Economic Journal, 49:14-33.

229

REFERENCES (Others)

• Lucas, Robert E., Jr (1988), “The mechanics of economic development”, Journal of Monetary Economics, 22:3-42.

• Romer, Paul M. (1990), “Endogenous technological change”, Journal of Political Economy, 98:71-102.

• Schumpeter, Joseph A. (1942). The theory of economic development. Harvard University Press.

• Solow, Robert M. (1956), “A contribution to the theory of economic growth”, Quarterly Journal of Economics, 70:65-94. 230

REFERENCES (Others)

• Solow, Robert M. (1957), “Technical change and the aggregate production function”, Review of Economics and Statistics, 39:312-320.

231

REFERENCES (Personal work)

• Kraay, Aart and Jaume Ventura (2000), “Current accounts in creditor and debtor countries”, Quarterly Journal of Economics 115:1137-1166.

• Lane, Philip R., and Gian Maria Milesi-Ferretti (2007), “The external wealth of nations mark II: revised and extended estimates of foreign assets and liabilities, 1970-2004”, Journal of International Economics 73: 223-250.

232


• Erauskin, Iñaki (2008), “The sources of economic growth in Spain, the Basque Country, and Navarre during 1986-2004”, Investigaciones Regionales, 12:35-58.

• Erauskin, Iñaki (2011), “Accounting for growth in Spain, the Basque Country (and its three historic territories), Navarre, and Madrid since 1965”. Ekonomiaz, 78:272-309. 233


• Erauskin, Iñaki (2009), “The current account and the new rule in a not-so-small open economy”, InvestigacionesEconómicas, vol. XXXIII(3):529-557.

• Erauskin, Iñaki (2015), “Savings, the size of the net foreign asset position, and the dynamics of current accounts”, International Review of Economics and Finance, 39: 353-370. 234

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